Conceptualizing and measuring instructional quality in mathematics education: A systematic literature review

Abstract

Conceptualizing and measuring instructional quality is important to understand what can be understood as “good teaching” and develop approaches to improve instruction. There is a consensus in teaching effectiveness research that instructional quality should be considered multidimensional with at least three basic dimensions rather than a unitary construct: student support, cognitive activation, and classroom management. Many studies have used this or similar frameworks as a foundation for empirical research. The purpose of this paper is to investigate the relation between the conceptual indicators underlying the conceptual definitions of the quality dimensions in the literature, and the various operational indicators used to operationalize these factors in empirical studies. We examined (a) which conceptual indicators are used to conceptualize the basic dimensions theoretically, (b) to which extent the operational indicator in the literature cover these conceptual indicators, and (c) if which additional indicators are addressed by the measurement instruments, which are not part of the theoretical conceptualization. We conducted a systematic literature review on the conceptualization and operationalization of Instructional Quality in Primary and Secondary Mathematics Education based on PRISMA procedures. We describe the span of conceptual indicators connected to the three basic dimensions over all articles (a) and analyze to which extent the measurement instruments are in line with these conceptual indicators (b, c). For each measurement dimension, the identified quality dimensions identified are, taken together, largely representative of the conceptual indicators connected to the core factor, but also a number of critical misconceptions occurred. Our review provides a comprehensive overview of the three basic dimensions of instructional quality in mathematics based on theoretical conceptualizations and measurement instruments in the literature. Beyond this, we observed that the descriptions of a substantial amount of quality dimensions and their conceptualizations did not clearly specify if the intended measurement referred to the learning opportunities orchestrated by the teacher, or the utilization of these opportunities by students. It remains a challenge to differentiate measures of instructional quality (as orchestrated by the teacher) from (perceived) teacher competencies/knowledge, and students’ reactions to the instruction. Recommendations are made for measurement practice, as well as directions for future research.

The subject matters for the professional vision of classroom management: an exploratory study with biology and mathematics expert teachers

“…Thus, continuous behavioral management in terms of monitoring student behavior and engagement might be particularly important for mathematics teachers. Such an emphasis on behavioral management can also be found in instructional quality frameworks for mathematic education (Mu et al, 2022). Further research is needed that replicates and complements our findings by investigating teachers from other subject areas and stimuli that display settings that vary with respect to how typical they are for the respective subjects.…”

“…However, subject-specific aspects might need to be added or specified due to typical activities in a subject: For instance, ensuring student safety or the management of material or the room are aspects of classroom management that are particularly important for science teachers (Praetorius et al, 2020). Such aspects of the organization of the classroom or the learning environment are rarely considered in frameworks of instructional quality in mathematics education, which are often more focused on behavioral management (Mu et al, 2022). Similarly, the majority of pre-service teachers share the belief that the subject impacts how a classroom is managed (Kwok, 2021).…”

“…Besides differences with respect to typical classroom management events, some subjects might also require more classroom management addressing student safety and the management of the room and the material (e.g., science; Praetorius et al, 2020). In contrast, other subjects may call for more shortterm monitoring of student behavior and learning progress (e.g., mathematics; Kwok, 2021;Mu et al, 2022). If we accept that subjects differ with respect to typical classroom management events and typical demands on teachers' management, it stands to reason that even with respect to the generic aspect of classroom management, experts from different subjects will and should develop a different, subject-specific TPVCM.…”

Building Conceptual Understanding of Multiplicative Reasoning Content in Third Graders Struggling to Learn Mathematics: A Feasibility Study

“…To document and measure fidelity of implementation, we developed two measures (see Figure S1 in Appendix B of online supplementary materials for the fidelity instrument). The first addressed overall quality of instruction (e.g., uses clear and mathematically precise language, manages instructional time effectively) based on attributes of effective teaching (Mu et al., 2022). The second focused on procedural fidelity and adherence (e.g., uses strategic prompting or framing of questions to elicit students’ thinking during warm‐up tasks, follows student discussion of problem solution by explicitly identifying/highlighting key multiplication ideas and/or generalizations during exploration or problem tasks) to the MR intervention.…”

Unlocking Teacher Professional Performance: Exploring Teaching Creativity in Transmitting Digital Literacy, Grit, and Instructional Quality

“…Overall, instructional quality is a complex and multifaceted concept that requires careful consideration and assessment to enhance learning and teaching experiences [65,66]. Instructional quality also reflects classroom teaching characteristics that teachers manage and observe in a way that makes sense and is supported by empirical evidence that aligns with the development of student learning outcomes [67]. To date, finding an adequate definition of instructional quality has been quite difficult.…”